We introduce the Semiparametric Time Series Regression with Mixed Additive Spline Fourier (STSR–MASF) model as an innovative approach for analyzing time series data with complex patterns. The model combines the flexibility of the spline estimator in capturing nonlinear variations across specific sub-intervals and the strength of the Fourier series in representing periodically recurring patterns. Within the semiparametric regression framework, STSR–MASF integrates both linear parametric and nonparametric components, with the optimal number of knots and oscillations determined using the Generalized Cross-Validation (GCV) criterion. The model was trained and tested using Earth’s skin temperature data from the National Aeronautics and Space Administration (NASA) MERRA-2 for East Kalimantan, Indonesia, a tropical rainforest region. The results demonstrate that the STSR–MASF model provides more accurate estimations and forecasts compared to six previous methods proposed in earlier studies with highly accurate predictions. This innovation not only offers methodological advancements in nonlinear time series modeling, but also contributes practical insights into understanding variations in Earth’s skin temperature in tropical regions, supporting broader efforts toward global climate change mitigation.
Dani et al. (Mon,) studied this question.